Many high resolution measurement systems and experimental setups can be seriously affected by external vibration sources.
The dominant source will normally be building vibrations excited by machinery and passing traffic. Acoustic sources can also
be troublesome, as can forces introduced directly by the operators hand. With a plethora of solutions available for isolating
a system from the environment, how can one decide which is the right solution for a particular application?

A system can react resonantly and non-resonantly to external vibrations. Consider the case of the interferometer illustrated
below.

non-resonant

resonant

A low frequency vertical acceleration of the instrument will cause the structure to distort - the amplitude of this distortion
will be proportional to the acceleration and independent of frequency. At higher frequencies structural resonances can be
excited. For example a mirror holder can vibrate and thereby modulate the optical path length. In general both effects will
be present but which effect is more important will vary from system to system.

In a system where the structural resonances dominate it will be necessary to isolate against both, building vibrations and
acoustic sources. Since these structural resonances come at relatively high frequencies (>50HZ) it is possible to obtain
sufficient isolation by mounting the system on rubber inside an acoustic hood. Crude systems using tennis balls or basket
balls as isolation elements can be used successfully for such applications - but beware - this is the worst possible 'solution'
against low frequency building vibrations.

The vast majority of high resolution measurement instruments react to the distortions introduced by low frequency building
vibrations. For isolation against low frequency vibrations the simplest solution is to mount the system on a very soft spring.
The transmibility of a slightly damped spring is shown in the curve [A] below.

The characteristics of the spring are a transmissibility of unity at the lowest frequency fr. Beyound about 1.4x
fr, the spring begins to isolate with the transmission falling off proportional to the sqaure of the frequency.
It is important that the frequency fr lies low enough that it is in a region where no signigicant vibration energy
is present. Long elastic cords have been succesfully used, but the system is so resonant and so soft that it takes an agee to
settle down - only students have enough time on their hands! To improve the settling time some damping should be introduced.
Air support columns are widely available with optimally damped characteristics. These systems still however have the
disadvantage of being very soft and take several seconds to settle down after a disturbance. Note that is not possible to
arbitrarily increase the damping - too much damping as in curve [B] allows the resonance to be removed but the system becomes
'glued' to the floor via the damping medium and can no longer isolate at all!

Active isolation systems offer a solution which combines stiffness with a very short settling time. The most useful active
systems employ inertial velocity in a feedback loop. (Inertial velocity can be measured for example by integration the signal
from an accelerometer). A signal proportional to inertial velocity is very similar to a viscous damping force, but with the
very important difference that the damping is relative to an inertial plane. So in contrast to the passive system, by
increasing the damping as in curve [C] and [D], the system becomes 'glued' to the inerial plane which by definition means the
system is isolated from the environment. The more damping the better.

The advantages of active systems over passive ones are many:

small size

inherently stiff

rapid recovery from shock (1-10 ms)

no air required

no set-up time

a performance that is better than that of the best passive systems.

The price is generally modest - and a tiny fraction of the cost of the equipment that will sit on top of the system.